Infinite Crossed Products (eBook)

Front Cover 1
Infinite Crossed Products 4
Copyright Page 5
Contents 8
Preface 12
Chapter 1. Crossed Products and Group-Graded Rings 14
1. Crossed Products 14
2. Group-Graded Rings and Duality 23
3. Induced Modules 32
4. Maschke’s Theorem 42
Chapter 2. Delta Methods and Semiprime Rings 52
5. Delta Methods 52
6. Coset Calculus 61
7. Minimal Forms 69
8. Sufficient Conditions 80
9. Polynomial Identities 87
Chapter 3. The Symmetric Ring of Quotients 96
10. The Martindale Ring of Quotients 96
11. Separated Groups 107
12. X-Inner Automorphisms 118
13. Free Rings 130
Chapter 4. Prime Ideals – The Finite Case 144
14. G-Prime Coefficients 144
15. Prime Coefficients 155
16. Finite Groups and Incomparability 164
17. Primeness and Sylow Subgroups 176
18. Semiprimeness and Sylow Subgroups 189
Chapter 5. Prime Ideals – The Noetherian Case 200
19. Orbitally Sound Groups 200
20. Polycyclic Group Algebras 210
21. Polycyclic Crossed Products 221
22. Jacobson Rings 233
23. P. I. Algebras 245
Chapter 6. Group Actions and Fixed Rings 254
24. Fixed Points and Traces 254
25. Integrality 267
26. Finiteness Conditions 277
27. Rings With No Nilpotent Elements 289
28. Prime Ideals and Fixed Rings 298
Chapter 7. Group Actions and Galois Theory 310
29. Traces and Truncation 310
30. The Galois Correspondence 322
31. Almost Normal Subgroups 332
32. Free Rings and Subrings 343
Chapter 8. Grothendieck Groups and Induced Modules 356
33. Grothendieck Groups 356
34. Graded Rings 369
35. Group Extensions 380
36. The Induction Theorem 391
Chapter 9. Zero Divisors and Idempotents 404
37. Zero Divisors and Goldie Rank 404
38. The Zalesskii-Neroslavskii Example 418
39. Almost Injective Modules 431
40. Stably Free Modules 443
References 458
Index 472